No I don't really think so, someone can be an evil genius but hopeless at interpersonal stuff, so high Int plus evil doesn't make you a manipulator. Consider a mad scientist who's the henchman of a supervillain for example. So high Int plus evil shouldn't mean you're automatically good at manipulating people.
As for the other traits, consider Trump as the example. He has a knack for exploiting people but would you say he's particularly wise or intelligent? So that leaves Cha as the trait to describe Trump, a single dimension. But does he really exude charm? I don't think so, so I think interpersonal traits need at least an extra dimension.
Int and Wis describe two sides of internal intelligence, so having two sides of interpersonal intelligence could help too. For example, Cha would be traditional Charisma, the natural ability to exude charm and influence people, but Cunning would work the other way, it would be the ability to "read" people. Someone with the Cunning trait would make up for a lack of charisma by using trickery, but they wouldn't necessarily have book-smarts intelligence or be wise like a priest.
As an example why I think the three-value system isn't sufficient consider someone based on the Dalai Lama archetype. They could have high Int, high Wis, high Cha, but they could also be naive about evil in others, so for example they take a chance on someone then that person betrays them. Should we say they lacked Wis then because they were fooled that way? the added "Cunning" trait would represent street smarts, cynicism, and the ability to detect ulterior motives. I think tacking all of these into Wis or something would limit the ability to tell different types of stories, for example a highly enlightened Zen Buddhist who took in a person who turns out to be evil and betrays them. It seems a little too reductionist to then say that the Buddhist must have been dumb or unwise then, unless all wise people are automatically distrusting cynics.